Abstract. The paper is devoted to studying the problem of controllability for 3D
Navier-Stokes equations in a bounded domain. We develop the method
introduced by Agrachev and Sarychev in the 2D case and establish a
sufficient condition under which the problem in question is
approximately controllable by a finite-dimensional force. In the
particular case of a torus, it is shown that our sufficient condition
is fulfilled for a control of low dimensio